Breakdown of the electric dipole approximation at Cooper minima in direct two-photon ionisation

J Hofbrucker,S Fritzsche,A V Volotka

doi:10.1038/s41598-020-60206-z

Abstract

We predict breakdown of the electric dipole approximation at nonlinear Cooper minimum in direct two-photon K–shell atomic ionisation by circularly polarised light. According to predictions based on the electric dipole approximation, we expect that tuning the incident photon energy to the Cooper minimum in two-photon ionisation results in pure depletion of one spin projection of the initially bound 1s electrons, and hence, leaves the ionised atom in a fully oriented state. We show that by inclusion of electric quadrupole interaction, dramatic drop of orientation purity is obtained. The low degree of the remaining ion orientation provides a direct access to contributions of the electron-photon interaction beyond the electric dipole approximation in the two-photon ionisation of atoms and molecules. The orientation of the photoions can be experimentally detected either directly by a Stern-Gerlach analyzer, or by means of subsequent Kα fluorescence emission, which has the information about the ion orientation imprinted in the polarisation of the emitted photons.

Highlights

We predict breakdown of the electric dipole approximation at nonlinear Cooper minimum in direct two-photon K–shell atomic ionisation by circularly polarised light
That a similar Cooper minimum is present in total cross sections of multi-photon ionisation processes[38,39,40], where it appears in a form of a local minimum
The concept of Cooper minimum was generalised to two-photon ionisation of inner-shell electrons, where it originates from fine-structure splitting of the 2p shell into the 2p1/2 and 2p3/2 subshells

Summary

Introduction

We predict breakdown of the electric dipole approximation at nonlinear Cooper minimum in direct two-photon K–shell atomic ionisation by circularly polarised light. Such a Cooper minimum arises at a incident photon energy, where the dominant dipole element passes through a local minimum This minimum does influence the shape of the total cross section, but more significantly, can strongly affect the photoelectron angular distributions[32]. It has been shown theoretically before[33,34], that strong anisotropic effects can be observed near Cooper minima due to relativistic and correlation effects, which are necessary to explain experimental measurements[32,35,36]. Instead of solely detecting the yields, we suggest to carry out measurements of degree of polarisation of photoions or fluorescence photons

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Conclusion